Graph y=2tan(x)

Problem

y=2*tan(x)

Solution

1. Identify the parent function and its properties. The base function is y=tan(x) which has a period of π and vertical asymptotes at x=π/2+n*π for any integer n

2. Determine the transformation applied to the parent function. The coefficient 2 in y=2*tan(x) represents a vertical stretch by a factor of 2

3. Locate the vertical asymptotes. Since there is no horizontal shift or change in period, the asymptotes remain at x=−π/2 x=π/2 x=(3*π)/2 and so on.

4. Identify key points for one period. In the interval (−π/2,π/2) the graph passes through the origin (0,0) Because of the vertical stretch, the points normally at (−π/4,−1) and (π/4,1) move to (−π/4,−2) and (π/4,2)

5. Sketch the curve through the identified points. Draw a smooth curve that approaches the vertical asymptotes, passing through (−π/4,−2) (0,0) and (π/4,2) then repeat this pattern for every period of π

Final Answer

y=2*tan(x)

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